Excitons and biexcitons in semiconductor quantum wires

The exciton and biexciton ground-state binding energies are calculated for semiconductor quantum wires of radius R smaller than the bulk exciton radius $a_0$ assuming an infinite confining potential. Both the excitonic and biexcitonic (molecular) binding energies are enhanced by a factor greater than 5 for GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As quantum wires of radius approximately $a_0$/2. The simultaneous shrinking of the exciton size with the wire radius is shown to reduce the contribution (when compared with the quasi-two-dimensional case) of dielectric polarization effects which arise when the wire is embedded in a cladding with a lower dielectric constant.